Properties

Label 9680.r
Number of curves $4$
Conductor $9680$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 9680.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9680.r1 9680w4 \([0, 0, 0, -114587, 14925834]\) \(22930509321/6875\) \(49887157760000\) \([4]\) \(30720\) \(1.6064\)  
9680.r2 9680w3 \([0, 0, 0, -56507, -5049814]\) \(2749884201/73205\) \(531198455828480\) \([2]\) \(30720\) \(1.6064\)  
9680.r3 9680w2 \([0, 0, 0, -8107, 167706]\) \(8120601/3025\) \(21950349414400\) \([2, 2]\) \(15360\) \(1.2599\)  
9680.r4 9680w1 \([0, 0, 0, 1573, 18634]\) \(59319/55\) \(-399097262080\) \([2]\) \(7680\) \(0.91328\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9680.r have rank \(0\).

Complex multiplication

The elliptic curves in class 9680.r do not have complex multiplication.

Modular form 9680.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{5} - 3 q^{9} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.